We study self-similar analytical solutions for force-free magnetic field in azimuthal symmetry and arcade topology. We assume the existence of a poloidal magnetic field, anchored on a heavy spherical conductor. The field is changed by shearing the foot points of the arcade due to differential rotation. This rotation gives rise to a toroidal component in the magnetic structure which reacts by ex...

References 2.full.html#ref-list-1 http://rspa.royalsocietypublishing.org/content/469/2156/2013002 This article cites 34 articles, 8 of which can be accessed free Subject collections (164 articles) mechanical engineering • Articles on similar topics can be found in the following collections Email alerting service here the box at the top right-hand corner of the article or click Receive free ema...

The purpose of this paper is to give the flavor of the subject of self-similar tilings in a relatively elementary setting, and to provide a novel method for the construction of such polygonal tilings.

An iterated function system consisting of contractive similarity mappings has a unique attractor F ⊆ R which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling T of the convex hull of the attractor. These tiles form a collection of sets whose geometry is typically much simpler than tha...